Observable versus unobservable R&D investments in duopolies

We study a quantity-setting duopoly with homogeneous products in which two firms first make their cost-reducing R&D investments, and then compete in quantities. When making its R&D investment, each firm is uncertain about its R&D outcome. Its new marginal cost is probabilistically determined later, but before the firm chooses its output level. When choosing its output level, each firm has private information regarding its own new marginal cost. We develop the observable-investments and the unobservable-investments models. We compare the outcomes of these two main models, and perform comparative statics of them with respect to each of the parameters, respectively. As variations, we consider the observable-investments and the unobservable-investments model based on a price-setting duopoly with product differentiation.